Second order Definition and 602 Threads

Homework Statement http://books.google.co.uk/books?id=93b3cjVJ2l4C&lpg=PA135&ots=8OtqgKwrQ2&dq=%22Two%20particles%20are%20connected%20by%20a%20spring%20of%20spring%20constant%20k%22%20and%20zero%20equilibrium%20%20length&pg=PA136#v=onepage&q&f=false Homework Equations All in the link...

Homework Statement Attached. If you don't mind I'd like to go through each part of the question to make sure I've understood correctly. Thanks a lot :smile: Homework Equations F=qE F=(γq^2)/(d^2) F=Kx Taylor/Maclaurin (?) The Attempt at a Solution So for part (a) I know that...

Hey, I'm not sure how to even approach this problem. It's not a simple ODE. Basically, I want to find the solution for Θ in terms of ε. The equation is \frac{1}{ε}*\frac{d}{dε}*(ε*\frac{dΘ}{dε})-β^{2}Θ=0 I tried to move the B^2 to the other side and I wasn't able to solve it that way. I...

Homework Statement For second order circuits, do you apply kcl/kvl in the circuit when the switch is open or closed to find the differential equation for complimentary solution? For example for the circuit attached (the circuit has been operating for a long time with switch closed prior...

Homework Statement Solve: [ d^2y1/dx^2 ] = [ a -a ] [ y1 ] [ d^2y2/dx^2 ] [ -a a ] [ y2 ] A = [ a -a ] [ -a a ] Homework Equations Everything required is in (1) above The Attempt at a Solution Reduce to 1st order system M = [ 0 I ] [ A 0 ] Hence, M = [ 0 0 1...

This is a problem from Boyd Nonlinear Optics chptr 1 problem 2. Homework Statement Numerical estimate of nonlinear optical quantities. A laser beam of frequency ω carrying 1 W of power is focused to a spot size of 30μm diameter in a crystal having a refractive index of n =2 and a second order...

Hello everyone I just want to ask why In a centrosymmetric media the media doe not change why going from r to -t r is a position vector thus Second order susceptibility becomes zero ?? Thank you

Hello all, I need to find the second order derivative of w by t, and to calculate it's value at t=1. This is what I know about w, x and y. \[w=ln(x+y)\] \[x=e^{t}\] \[y=e^{-t}\]The answer in the book is: \[\frac{4}{(e^{t}+e^{-t})^{2}}\] I got another answer and I don't know what I did...

Homework Statement y^{\prime\prime}+y=\frac{1}{\sin x} Homework Equations The Attempt at a Solution I solved the homogenous equation: y=C_1\sin x+C_2\cos x, and then I tried to use method of variable the constant. But the equation system is rather hard. Do you know any other...

This isn't a homework question per se. Am merely seeking an explanation how the method of characteristics may be applied to a second order PDE. For instance, how is it used to solve utt=uxx-2ut?

Reading my first calculus course at my first semester as an "Computer Engineer". In Sweden it's called "Single Variable Calculus". I have my first exams next week and i have been solving differents of DE's. y'-3y'+2y = 2ex But now i have encountered a problem in my "partikulär lösning"...

$$ xy'' - y' = 3x^{2} $$ $$ y' = p $$ $$ y'' = p' $$ $$ xp' - p =3x^{2} $$ $$ p' - \frac{1}{x}p = 3x $$ after multiplying by the integrating factor we get.. $$ \frac{1}{x}p' - \frac{1}{x^{2}}p =3 $$ so $$ [\frac{1}{x}p]' = 3? $$ I know that these two below are equal, but can someone please show...

Homework Statement If d^2s/dt^2 = a, given that ds/dt = u and s = 0, when t = 0, where a, u are constants show that s = ut + .5at^2 2. The attempt at a solution du/dt = a cross multiplying and then integrating and we get u = at ds/dt = at cross multiply and...

EDIT: my problem is solved, thank you to those who helped Homework Statement Solve: x y^{\prime \prime} = y^{\prime} \log (\frac{y^{\prime}}{x}) Note: This is the first part of an undergraduate applications course in differential equations. We were taught to solve second order...

Hello (Smirk) Given the x^{2}y''+axy'+by=0,I have to show that with replacing x with e^{z},it becomes a second order differential equation,with constant terms. I tried to do this and I got this: y''+\frac{a}{e^{z}}y'+\frac{b}{e^{2z}}y=0 . But,at this equation the terms aren't constant...

See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.

Homework Statement Solve the initial value problem y''-y'-2y=0 y(0)=β , y'(0)=2. Then find β so that the solution approaches zero as t→∞ Homework Equations R^2-R-2=0 C1+C2=β, -C1+2C2=2 The Attempt at a SolutionI solved the equation got the r- values 1 and -2 , then i solved the two equations...

Hello all, I have a geodesic equation from extremizing the action which is second order. I am curious as to what the significance is of having 2 independent geodesic equations is. Also I was wondering what the best way to deal with this is.

Homework Statement y''+6y=f(t), y(0)=0, y'(0)=-2 f(t)= t for 0≤t<1 and 0 for t≥1 Homework Equations The Attempt at a Solution L{y''}+6L{y}=L{t}-L{tμ(t-1)} where μ(t-1) is Unit Step Y(s)=L{y} sY(s)-y(0)=L{y'} and y(0)=0 s2Y(s)-sy(0)-y'(0)+6Y(s) where y(0)=0 and...

Homework Statement Let y(x)=\sumckxk (k=0 to ∞) be a power series solution of (x2-1)y''+x3y'+y=2x, y(0)=1, y'(0)=0 Note that x=0 is an ordinary point. Homework Equations y(x)=\sumckxk (k=0 to ∞) y'(x)=\sum(kckxk-1) (k=1 to ∞) y''(x)=\sum(k(k-1))ckxk-2 (k=2 to ∞) The Attempt at a Solution...

Homework Statement This was an electrical engineering lab, dealing with the steady state response of an RLC circuit (diagram attached). The main part of the lab consisted of experimentally determining the circuit's critical resistance value, and viewing the overdamped and underdamped...

Homework Statement "Solve differential equation y''+y=2*cos x. Draw circuit of the equation and think about the strange behavior of the current." The attempt at a solution I was able to solve the equation, but I have no idea how to draw circuit about it, we haven't gone through this...

Homework Statement Solve the following DE y'' + 8y' − 9y = 0, y(1) = 1, y'(1) = 0 Homework Equations Homogenous DE with constant coefficients The Attempt at a Solution Well, i solved it normally using a CE and having yH= c1 e^t + c2 e^(-9t) .. y' = c1 e^t -9 c2 e^(-9t)...

Hello everyone, I'm having trouble understanding the solutions to DE's of the form: ay''+by'+cy=f(t) We've gone over them in class, I've talked with my friends, and it just doesn't make any sense to me. I was wondering if anyone on here would help me understand the solutions, it would be...

Hi MHB. I'm having yet another doubt regarding differential equations. Can someone please help me out? Thanks. Consider the following differential equation: {y}''+{y}'= x^{2} I have found the homogeneous solution to be: y_{H}=c_{1} + c_{2}e^{-x} But when finding the particular solution...

Hey guys , having a bit of bother getting a solution for this question. Any help would be greatly appreciated! There is a Picture attached showing how far I have got ..

Homework Statement Solve d^2x/dt^2 = (3x^3)/2 when dx/dt = -8 and x = 4 when t = 0 2. The attempt at a solution v = dx/dt dv/dx = d^2/dx^2 d^2x/dt^2 = v(dv/dx) = (3x^3)/2 v dv = (3x^3)/2 dx integrating and using limits and you get : v^2/2 -32 = (3x^4)/8 - 96 ...

Homework Statement Solve (d^2x)/(dt^2) = 2x(9 + x^2) given that dx/dt = 9 when x = 0 and x = 3 when t = 0 Homework Equations The Attempt at a Solution v = dx/dt ...... dv/dx = d^2x/dt^2 dv/dx = v(dv/dx) v(dv/dx) = 18x +2x^3 integrating and evaluating using...

Homework Statement Hi, I think this is called second order.So I'm working on a problem I haven't had lecture yet. I'm trying to understand. Oh wait here is problem. Someone can help me understand this sort of problem in general. For what values of k does the function y = coskt satisfy...

Homework Statement y''+3y'+3.25=3cost-1.5sintHomework Equations yh = e(a/2)t(Acost+Bsint) yp = Kcos(ωt)+Msin(ωt) [when r(x)=kcos(ωt) or ksin(ωt)]The Attempt at a Solution I got the homogeneous solution, which is e-1.5t(Acost+Bsint) but I am having trouble with the particular solution. I...

If we have \frac{1}{X(x)} \frac{d^2 X}{dx^2}=-κ^2, the literature is saying that the solution must be: e^(±iκx), but am always getting e^(±k^2x). Isn't the approach is to decently integrate twice and then raise the ln by the exponential? Where am I going wrong? Thanks

Solving a "simple" second order PDE, do I need the Fourier? Homework Statement The problem as given: y'' + 2y' + 5y = 10\cos t We want to find the general solution and the steady-state solution. We're using \mu y'' + c y' + k y = F(t) as our general form. OK, so I first want the general...

Homework Statement A mass of 5kg stretches a spring 10cm. The mass is acted upon by an external force of 10sin(t/2) Newtons and moves in a medium that imparts a viscous force of 2N when the speed of the mass is 4cm/sec. If the mass is set in motion from its equilibrium position with an initial...

Hi, I derived the equation: 1+(y')^2-y y''-2y\left(1+(y')^2\right)^{3/2}=0 Letting y'=p and y''=p\frac{dp}{dy}, I obtain: \frac{dp}{dy}=\frac{1+p^2-2y(1+p^2)^{3/2}}{yp} I believe it's tractable in p because Mathematica gives a relatively simple answer: p=\begin{cases}\frac{i...

Much like Simpson's Rule, a.k.a. the prismoidal method, improves upon the trapezoidal method by fitting parabolic arcs across known discrete points on some function $f(x)$ rather than line segments, Newton-Cotes formulas of order 1 and 2 fit cubic and quartic curves across points on the curve...

I had made a post in the past about the same problem and unfortunately I wasn't clear enough so I am trying again. I am studying an article and there I found without any proof that the solution of: Let ##g \in \mathbb{C}## and let ##u:(0,\infty)\to \mathbb{C}## $$ -u''+\lambda^2u=f\,\, on...

I have a small problem in solving a Second Order Linear Constant Coefficient Differential Equation. Please see the attached image. I understand upto the point above the arrow. What I don't understand is how he got dy/dx = 9

-u''(z)+α2u(z)=f(z), u(0)=g(z), u(z)=0 as z→∞ -u''(z)+α2u'(z)=f(z), u(0)=g(z), u(z)=0 as z→∞ I am interested to solve these two boundary problems using Green's functions. It is noticed that z is complex variable. Can someone help me to do this?

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Hello I need to plot this simple system: x'' = -x using midpoint Euler. u1 = -x , u2 = -x' u1' = u2 u2' = -x u1(n+1) = u1(n) + h*? u2(n+1) = u2(n) + h*f((1/2)*(u1(n) + u1(n+1)) We don't know u1(n+1). I tried approximating it with u1(n+1) = u1(n) + h*u2(n) u2(1+i) =...

Hi could do with a little help with this question please! The question A damped oscillation with no external forces can be modeled by the equation: \frac{d^2x}{dt^2}+2\frac{dx}{dt}+2x=0 Where x mm is amplitude of the oscillation at time seconds. The initial amplitude of the...

Homework Statement Find the general solution to the differential equation y'' -16y = 0, where y is a function of x. Give initial conditions that would give a unique solution to the eqution. For the differential equation y'' - k2y = R(x), with k ≠ 0 a real constant, show that it has a...

Find a solution to the following second order differential equation xy'+y=1/y^2 My Attempt: P= y'= dy/dx x dy/dx + y = 1/y^2 dy/dx + y/x = 1/xy^2 Integrating Factor = e^∫1/x dx = e^lnx y e^lnx=∫ (e^lnx)(1/xy^2) dx

I'm trying to create a java application that models the path of a double pendulum. To do so I have been attempting to use Lagrangian Mechanics to find the equation's of motion for the system. The problem is that I have never seen a set of equations like the one yielded by this method and need...

Hi Everbody, I am having a bit of trouble with an AS Physics question regarding diffraction gratings. I have managed to solve the problem that I have been facing, although I am not completely sure that I got to it through the correct means, and also why the answer is such. Homework...

Hello! It is the first time that i write on this forum. I'm doing a PhD but i can't solve this equation: it's a non-linear second order differential equation. ay''+b|y|y'+cy+dx=0 Some ideas?

Homework Statement The question is such : System is modeled as : y''+2y'+4y=u(t) find the time at which the system goes up 75,90,95 % of its final value.Homework Equations The Attempt at a Solution I have no idea how to touch that,I tried to find the source of the regular rise time (from 10...

Homework Statement y''-2y'+2y = e^-t, y(0)=0, y'(0)=4 Homework Equations The Attempt at a Solution Again.. I find it to be really easy, then get it wrong. My answer is not even close. Applying the properties of the laplace transform in the usual way, s^2L{y} - 4 - 2L{y} + 2L{y} = L{e^-t}...

Homework Statement Hello, maybe this is due to my lack of understand of RK4, but I have an equation: x'' + b^2*x=0 (derivatives with respect to variable t) and I need to use RK4 to find the solution on an interval. I can readily find solutions analytically, but my understanding of RK4...

Homework Statement Find the general solution for the following differential equation: y'' + x(y')^2 = 0. Homework Equations Integration, differentiation... The Attempt at a Solution Usually for these sort of DE you could use the substitution v(x) = y'(x) and this would simplify...